Abstract
We systematically search for classical open string solutions in AdS3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.
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